文档介绍：复杂网络上的损伤扩散研究●损伤扩散技术●动力学规则●损伤扩散技术的演化模式●二维 Ising 点阵上的损伤扩散●works ●三角形小世界网络的构成●三角形小世界网络上的 Damage spreading 内容提要 Damage Spreading <Random growth processes The shape of a snowflake, the roughness of a crack surface, corroding process in iron, virus spreading, economic and social phenomena <Growth models: percolation, the damage spreading (DS) <The damage spreading (DS) Simulation of the time evolution of perturbation spreading throughout a cooperative system 损伤扩散方法 Damage spreading(DS )方法通过比较处于相同热噪声的两个系统( A、B,开始时存在微小差别)的时间演化的差别来研究影响系统演化的关键因素。 DS 技术的核心思想是通过两个系统上节点或单元( cell )的差别(或节点或单元上自旋的差别)来定义损伤,它的主要测度是系统的损伤密度,即 Hamming 距离(一般为平均值)。)1( 1)( 1 )( ),(???? Ni tsts Bi AiN tD?< Simulation method: Monte Carlo method · A evolves to equilibrium · A replica B of the system is made · At t =0, the spin in the center cell of the lattice B is flipped (damaged) and fixed all the time · A and B evolve with time > Theory The Hamiltonian : The Hamming distance : ji ijssJH???)1( 1)( 1 )( ),(???? Ni tsts Bi AiN tD?),'()1(),'(),'(ssWpsspW ssW K G???)( ),'( 1 ,,,, ''2 '21 '1sw ssW i Ni ssssssss G NN ii?????????)( ),'( ),( ,,,,, '''2 '21 '1sw ssW ij ji ssssssssss K NN ijji??????????)] exp( ,1 min[ )(Tk E sw B i i???????????0,1 0,0)( ij ij ijE for E for sw Glauber -Kawasaki dynamics Damage Spreading : what have we learnt? d and T c :the heat-bath dynamics T d coincides with T c whereas for Glauber and Metropolis dynamics T d is near but smaller than T c2. Elements considered:the interactions ( ferro , antiferro , spin glass ,etc.), the Monte Carlo rules (heat bath , Glauber , Metropolis , etc.), the lattice geometry ( square , triangle , cubic , etc.), the symmetry of the spin variables and the external conditions (., ic field ). 3. DS is less sensitive to statistical fluctuations is sensitive to the ways of updating 5. DS is sensitive to dynamics Damage Spreading: problems unsolved d and T c :explanation to determine T d (T